A systematic analysis of the problem of determining optimal feeding strategies for immobilized enzyme reactions in fed batch bioreactor is presented in this paper. The optimal control theory is applied to a heterogeneous bioreactor model consisting of a bulk liquid phase and an immobilized enzyme phase. The optimal feeding policy and singular interval are obtained in terms of state variables alone. It is shown that a constantly fed bioreactor operation is optimal for a process whose kinetics depends on the single reactant concentration. The analytical results are supplemented with a numerical example of deacylation of penicillin G. Effects of various operating conditions, such as reactant feed concentration, enzyme loading and diffusional limitation, on the optimal performance of the bioreactor is illustrated.